Characteristic value determination from small samples

The paper deals with the characteristic value determination from relatively small samples. When the distribution and its parameters of a random variable are known, the characteristic value is deterministic quantity. However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples. Therefore the characteristic value is by itself a random variable. The estimates of characteristic values are strongly dependant on the distribution of random variable. In the paper we show the analytical solution for characteristic value determination from random samples of normal and lognormal random variables. The confirmation of analytical results is accomplished by the use of computer simulations. For Gumbel, and Weibull distribution the characteristic value estimates are obtained numerically by combination of simulations and bisection method. In the paper the numerical results are presented for 5% characteristic values with 75% confidence interval, which is in accord with the majority of European building standards. The proposed approach is demonstrated on the data of experimentally obtained bending strengths of finger jointed wooden beams.